N.Y. Uniform District Court Act Law § 1303

§ 1303. Jury trial; how obtained; jury fee.\n (a) Either party after joinder of issue may demand a trial by jury.\nThe demand must be made in writing and must be filed with the clerk with\nthe notice of trial set forth in § 1301. Any other party to the action\nwithin ten days after the service of a copy of the notice of trial upon\nhim unaccompanied by a written notice demanding a trial by jury, may\nserve upon the attorneys for all the other parties to the action a\nwritten notice demanding a jury trial and file a copy of such notice\nwith the clerk within three days after service thereof. In a summary\nproceeding to recover possession of real property, the demand may be\nmade by the tenant at the time of answering or by the landlord at any\ntime before the day of trial.\n (b) Unless a demand is made and the jury fee paid as provided in\nsection nineteen hundred eleven of this act, a jury trial is waived.\n (c) The court may relieve a party from the effect of failing to comply\nwith this section if no undue prejudice to the rights of another party\nwould result.\n